L2-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian

This paper deals with a fourth order parabolic PDE arising in the theory of epitaxial growth of crystal. We focalize the study on one open question proposed by Escudero et al. (2015) [4], that is, Lp-norm blow-up. For the initial energy J(u0)<λ16‖u0‖22, we prove the solution blows up in finite time with L2-norm, where λ1 is the least Dirichlet eigenvalue of the biharmonic operator. Moreover, the lifespan of the solution is got, and the results of this paper also generalize the results got by Xu and Zhou (2017) [12].